pdfcau {lmomco} | R Documentation

## Probability Density Function of the Cauchy Distribution

### Description

This function computes the probability density of the Cauchy distribution given parameters (xi and α) of the distribution provided by `parcau` or `vec2par`. The probability density function of the distribution is

f(x) = (π α [1 + ({frac{x-xi}{α}}^2)] )^{-1} mbox{,}

where f(x) is the probability density for quantile x, xi is a location parameter and α is a scale parameter.

### Usage

    pdfcau(x, para)

### Arguments

`x` | A real value.
`para` | The parameters from `parcau` or `vec2par`.

### Value

Probability density (f) for x.

### Author(s)

W.H. Asquith

### References

Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments: Computational Statistics and Data Analysis, vol. 43, pp. 299–314.

Evans, Merran, Hastings, Nicholas, Peacock, J.B., 2000, Statistical distributions: 3rd ed., Wiley, New York.

Gilchrist, W.G., 2000, Statistical modeling with quantile functions: Chapman and Hall/CRC, Boca Raton, FL.

### See Also

`cdfcau`, `quacau`, `parcau`, `vec2par`

### Examples

      cau <- vec2par(c(12,12),type='cau')
      x <- quacau(0.5,cau)
      pdfcau(x,cau)

[Package lmomco version 0.92 Index]